Weighing the baby at the clinic was a problem. The baby would not keep still and caused the scales the wobble.

So I held the baby and stood on the scales while the nurse read off $78 \; \text{kg}$.
Then the nurse held the baby while I read off $69 \; \text{kg}$.
Finally I held the nurse while the baby read off $137 \; \text{kg}$.

What is the combined weight of all three (in $\text{kg}$)?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.